Next Article in Journal / Special Issue
Recognition of Abnormal Uptake through 123I-mIBG Scintigraphy Entropy for Paediatric Neuroblastoma Identification
Previous Article in Journal
The Analytical Solution of Parabolic Volterra Integro-Differential Equations in the Infinite Domain
Previous Article in Special Issue
Study on the Inherent Complex Features and Chaos Control of IS–LM Fractional-Order Systems
Article Menu
Issue 10 (October) cover image

Export Article

Open AccessArticle
Entropy 2016, 18(10), 345; doi:10.3390/e18100345

A Novel Operational Matrix of Caputo Fractional Derivatives of Fibonacci Polynomials: Spectral Solutions of Fractional Differential Equations

1
Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah 21589, Saudi Arabia
2
Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt
*
Author to whom correspondence should be addressed.
Academic Editor: Carlo Cattani
Received: 28 July 2016 / Revised: 19 September 2016 / Accepted: 19 September 2016 / Published: 23 September 2016
(This article belongs to the Special Issue Wavelets, Fractals and Information Theory II)
View Full-Text   |   Download PDF [1282 KB, uploaded 23 September 2016]   |  

Abstract

Herein, two numerical algorithms for solving some linear and nonlinear fractional-order differential equations are presented and analyzed. For this purpose, a novel operational matrix of fractional-order derivatives of Fibonacci polynomials was constructed and employed along with the application of the tau and collocation spectral methods. The convergence and error analysis of the suggested Fibonacci expansion were carefully investigated. Some numerical examples with comparisons are presented to ensure the efficiency, applicability and high accuracy of the proposed algorithms. Two accurate semi-analytic polynomial solutions for linear and nonlinear fractional differential equations are the result. View Full-Text
Keywords: Fibonacci polynomials; operational matrix; spectral methods; modified Bessel functions; fractional-order differential equations; Van der Pol oscillator; Rayleigh equation Fibonacci polynomials; operational matrix; spectral methods; modified Bessel functions; fractional-order differential equations; Van der Pol oscillator; Rayleigh equation
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Abd-Elhameed, W.M.; Youssri, Y.H. A Novel Operational Matrix of Caputo Fractional Derivatives of Fibonacci Polynomials: Spectral Solutions of Fractional Differential Equations. Entropy 2016, 18, 345.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top